$\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a\cdot b} \\ \sqrt[n]{a}:\sqrt[n]{b}=\sqrt[n]{\frac{a}{b}} \\ \sqrt[n]{\sqrt[m]{a}}=\sqrt[{mn}]{a} \\ \\ \textbf{Gegeben:} \\ {a=36 \qquad b=53 \qquad m=3 \qquad n=7}\\ \\ \textbf{Rechnung:} \\ \sqrt[7]{36} \cdot \sqrt[7]{53} = \sqrt[7]{36\cdot 53}= \sqrt[7]{1,91\cdot 10^{3}}=2,94 \\ \sqrt[7]{36}:\sqrt[7]{53}=\sqrt[7]{\frac{36}{53}} = \sqrt[7]{\frac{36}{53}}=0,946 \\ \sqrt[7]{\sqrt[3]{36}}=\sqrt[{3\cdot 7}]{36}= \sqrt[21]{36}=1,19 \\ $